1. Certainty Equivalence and Precautionary Savings Consider a consumer facing the following finite horizon problem: max ES '4(1+p)'r TU(C,) where U(C,) = C -2' subject to C, + A, = Y, + (1+r,)A,_ A = 0 Note that ",, , and 4, are consumption, income and an asset at time t, and " is the return for the asset at time t and ? is the subjective discount rate. (a) Derive the stochastic Euler equation. From now on, suppose that ", = P Vi. (b) How can you represent the solution for " in terms of present and future incomes. (c) What is the impact of future uncertainty on the choice of C, ? (d) Replace the utility function with U(C, ) = 1-o where o is the risk-aversion parameter. What happens to your answer in (c)